The poem concerns the story of Adam and Eve and the Fall of Man, as the two original humans are tempted by the fallen angel Satan and expelled from the Garden of Eden.
It is no straightforward retelling of the Genesis story, however. Paradise Lost features Satan in several guises that present him as the hero. He is certainly a more interesting character than God, which has led critics to question whether the poem is in fact a criticism of the church's power.
This is very relevant to Northern Lights, with its depiction of the omnipotent "Magisterium" and the crimes that its power allows its authorities to commit.
The opening quote from Paradise Lost contains the title of the trilogy as a whole: "His Dark Materials". Pullman was greatly inspired by John Milton's work, and intended the trilogy to be a reflection of Paradise Lost – a battle between Heaven and Hell, with the devil in the role of the hero.
Presumably the Cabinet Council is the equivalent in Lyra's world to the British Parliament in our own. In which case, the Palace she is referring to may be the Palace of Westminster, seat of Parliament.
However, in Lyra's world the King is directly involved in politics, attending meetings of the Cabinet Council in person. This might suggest that the Palace in question is Buckingham Palace.
This line, along with the fact that the smell of the poppy later makes Lyra sleepy, suggests that it is consumed for its psychotropic effects. Poppies are the source of the drug opium, which was very popular in the Victorian era on which this world seems to be based.
Although it isn't mentioned specifically how the Scholars use the poppy, it's hinted that they eat it and so the effects of the drug would probably be fairly mild.
In both Lyra's world and our own, Yarnton is a town around 5 miles north of Oxford. Since in Lyra's world "anbaric" means electric, it seems that she is referring to the electricity substation that exists in real world Yarnton.
Lord Asriel is referring to the Collodion process, a 19th century photographic process now obsolete. Images were captured on glass plates coated with an emulsion of silver halides in gelatin.
The aurora borealis is a phenomena visible in the far north of our world and Lyra's.
An aurora is a natural light display, best seen in the polar regions, caused by the collision of charged particles directed by Earth's magnetic field.
In the Northern latitudes this is called aurora borealis after the Roman goddess of the dawn, Aurora, and the Greek name for the North wind, Boreas. It is also known as the Northern Lights.
The aurora becomes central to the plot of the novel, hence the British title of the novel.